We use a re-usable pour over cone filter for coffee. Small, lightweight (we also use it when backpacking), and makes a GREAT cup of coffee.
BTW - if using an inverter, divide watts by 10 to get a rough estimate of amperage. 1000W will pull close to 100 amps. Also, if you have a group 31 battery (~100 amp hours), you can draw it down to about 50%, which means it'll last for about half an hour at that rate with no other load. There are lots of other small loads though (refrigerator control circuit and propane solenoid, lights, water heater control circuit, igniter and solenoid, and more ...). Another big draw on the battery is the furnace - the blower motor draws a lot.